Hemoglobin gives blood its color when it reacts with different molecules. Oxygen reacts with the hemoglobin to produce a bright red color. This redness is found in the arteries and capillaries. In the veins the blood is deoxygenated which turns the blood a darker red with a bluish tinge.
The reason veins look blue has more to do with light diffusion from the skin and the process by which we register color than it does with the actual shade of blood.
For stage the darker tinge is the most often used because it the the color most often seen in life and easiest to recognize.
However, bright red blood used at the right moment can have a powerful psychological effect. For example, in Dracula the audience expects and waits for blood. If the first blood shown is bright, vibrant and healthy it will be exciting for the audience as well as for the vampire.
Choose your hue well, blood tells its own story and demands a huge amount of focus. It can be a powerful tool or a disastrous distraction.